A device for measuring the mass of a flowing medium is already known in which a hot wire is used as a temperature-dependent resistor, the hot wire being stretched substantially tautly over a plurality of support points within a sensor ring. Because of varying temperatures and soiling, particularly when the device is used in a motor vehicle, there is the danger of wire breakage as a result of the particular mode of operation of the hot wire. There is also the disadvantage that an irregular condition of heat away from the hot wire via the support points causes an undesirable impairment in the precision measurement of the device.